Calculus of Variations in the space L-infinity has a relatively short history in Analysis. The scalar-valued theory was pioneered by the Swedish mathematician Gunnar Aronsson in the 1960s and since then has developed enormously. The general vector-valued case delayed a lot to be developed and its systematic development began in the 2010s. One of the most fundamental problems in the area which was open until today (and has been attempted by many researchers) concerned that of the title. In this talk I will discuss the first result in this direction, which is based on joint work with my research associate Giles Shaw.